Simplifying Definition and 487 Threads

I have $\frac{sec\theta}{tan\theta}$. How can I simplify it to get $\csc\left({\theta}\right)$ ?

Homework Statement [/B] All voltages and impedances are in per unit values. After all the source transformations, why is the voltage source still 1 ? Homework EquationsThe Attempt at a Solution [/B]

Homework Statement I am given this circuit...

Hello all, I have this integral, and currently I'm evaluating it using Mathematica numerically, which takes time to be evaluated. Can I write it in a way that the integral has a formula in the Table of Integrals? \int_0^{\infty} F\left(a_1,a_2;a_3;a_4-a_5x\right) e^{-x}\,dx where...

Hi I'm trying to give myself a refresher in Leaving Cert maths and I'm running through some problems. Here's one which has me stumped (sorry I can't figure out how to show the actual symbols on the post, it's just showing as raw LaTEX when I try ) Combine terms and simplify the expression of -...

Homework Statement (A OR C) AND NOT(C AND A AND B OR C AND A AND NOT B) or (A + C) (CAB + CAB')' Relevant Equations (A+B)' = A'B' A(B+C) = (AB) + (AC) (AB)' = A' + B' The attempt at a solution I'm not sure how I'm suppose to expand (CAB + CAB')' for simplifying. I keep arriving at false which...

Dear forum, I'm new here (living in Arizona). I am stuck getting to derive this: F1−F2−F3 = 0, (2.1) F1c1−F2c2−F3c3 = 0, (2.2) F1z1−F2z2−F3z3 = 0. (2.3) Where the only unknowns are F2 and F3. The textbook states that F1, F2 and F3 can be eliminated to get: c1z3 −c1z2+c2z1 −c2z3 −c3z1 +c2z2 =...

Supposing I have $$(-4x^n)$$ Why does it equal $(-4)^n * x^n$ and not $(-4)^n * (-x) ^ n$? When we have a negative symbol it only applies to the first item in an expression? so $-xbcw$ equals $b * c * w * (-x)$? Which means if we wanted the other items to be negative we would have to do...

I have $$\frac{(-1)^n}{(4^n)n }(-4)^n$$ (where n is a sufficiently large positive number, I think in this case it only has to be positive). Is $\frac{-4^n}{4^n}$ the same thing as $(-1)^n$? How is this the case?

Homework Statement I got the problem down to: \frac{2}{\pi} \left[ \int_{0}^{\pi/2} \frac{2}{\pi}xsin(nx) dx + \int_{\frac{\pi}{2}}^{\pi} (\frac{-2}{\pi}x+2)sin(nx) dx \right] \frac{4}{\pi^2} \left[ \int_{0}^{\pi/2} xsin(nx) dx + \int_{pi/2}^{\pi} -xsin(nx) dx + \int_{pi/2}^{\pi} \pi...

I have $$-1 \le \cos\left({2x}\right) \le 1 $$ If everything is squared, it goes to $$0 \le \cos^2\left({2x}\right) \le 1 $$ and I'm not sure how $(-1)^2$ turns into $0$

I have this expression: $$\sqrt{ 1 - \frac{16}{\sqrt{x^2 + 16}}}$$ And the textbook simplifies it to $$\frac{x}{\sqrt{x^2 + 16}}$$ But I'm not sure how it does this.

I have this integral $$6\int_{}^{} \frac{u^3 - 1 + 1}{u - 1}\,d$$ And I need to simplify it to $$6\int_{}^{}u^2 + u + 1 \frac{1}{u - 1}\,du$$ But I don't know how to get to this step.

I have this integral: $$\int_{}^{} \frac{x^2}{x^2 + 9} \,dx$$ And I'm trying to simplify it to: $$\int_{}^{}\,dx - 9\int_{}^{} \frac{1}{x^2 + 9}\,dx$$ But I'm not sure of the steps necessary to do this.

I have this expression $$\frac {1} { e^x + \frac {1} {e^x}}$$ and it simplifies to $$\frac {e^x} { e^{2x} + 1}$$ And I'm not sure how to get this simplification or what rules to apply to get to this simplification.

Homework Statement This is a child thread I'm creating from a previous topic: https://www.physicsforums.com/threads/combinatorics-problem.871661/#post-5473920 In that thread, I was helped to come up with the expression for the number of arrangements of R distinct types of objects given the...

My question boils down to wondering if there is a way to simplify the imaginary part of a complex-valued function composed of n factors if the real and imaginary component for each of the factors is known but the factors may take on the value of their conjugate as well. For example, is there a...

I am trying to work through a simplication of this factorial with variables: (n/2)!/[(n+2)/2]! I get, 2[n(n-1)]/2[(n+2)(n+1)n(n-1)] cancelling the 2[n(n-1)] leaves me with 1/[(n+2)(n+1)] However, Wolfram Alpha tells me this can be simplified as 2/(n+2) and I don't see that. Thanks

The goal of this problem is to find the equivalent resistance of all the resistors. Each resistor shown in the image has a conductance of 1 mS which I believe is equal to 1000 ohms. I attached a picture of the circuit diagram in which I show some of my work in order to convey my erroneous...

(k + 7/k^2 + 6K + 9) + (k - 5/k^2 - 5k - 24)

I was supposed to simplify the expression ##\ln |\cot {x}|+\ln |\tan {x}\cos {x}|## and apparently it’s wrong. Where’s the mistake? Is it not simplified enough or . . . ? ##\ln |\cot {x}|+\ln |\tan {x}\cos {x}|## ##=\ln |\frac {\cos {x}}{\sin {x}}|+\ln |\frac {\sin {x}}{\cos {x}}\cdot \cos...

Homework Statement I'm trying to show that the output of this XOR circuit is ##F=A'B+AB'##, Homework Equations ##(A+B)'=A'\cdot B'## ##(A\cdot B)'=A'+B'## The Attempt at a Solution From the gates the output is ##[(A\cdot B)+(A+B)']'##, using De Morgan's laws this becomes ##[(A\cdot...

How is it equal to v in the end? I'm sorry for asking such questions. But I'm just trying to understand

Hello, I have already studied first year mathematics but I am doing some basic revision incase I missed anything, (I skipped two grades and am thus missing some small simple things I should know) When simplifying the single term expression, 2x^2y^2 times 5xy^4 my initial thought was they...

Homework Statement What physical quantity does ##\mathrm{J\cdot N\cdot W^{-1}\cdot kg^{-1}}## denote? Homework Equations You can simplify using mechanics equations or ones from electrodynamics. Be creative, I guess. The Attempt at a Solution ##\mathrm{J\cdot N\cdot W^{-1}\cdot kg^{-1}}##...

Homework Statement [/B] Simplify: \frac{5\cdot 8\cdot 11 \cdots (3i+2)}{2\cdot 5 \cdot 8 \cdots (3i-1)} Homework EquationsThe Attempt at a Solution I realize the numerator and denominator terms cancel besides the 2, however I'm struggling to write this in a proper form. Only just started...

Homework Statement Given that ##T = \frac{4E(V-E)}{4E(V-E)+V^2\sinh^2 (ka)}## Simplify the expression for T when a is large but not infinite, and again for the case when a tends to zero and the potential tends to infinity, such that ##d = Va## is a real constant. k is a constant, as is E...

Mod note: Moved from a homework section 1. Homework Statement Hello my question more has to do with theory that perhaps deals with algebra. Why is the following true? Homework Equations N/A The Attempt at a Solution N/A[/B]

In the attached picture, how is it justified to factor out an 'i' in the exponent of the 2 and the 5?

Homework Statement I have a tensor which is given by t_{ij} = -3bx_i x_j + b \delta_{ij} x^2 + c \epsilon_{ijk} x_k And now I am asked to calculate (t^2)_{ij} : = t_{ik} t_{kj} Homework EquationsThe Attempt at a Solution At first I thought I had to calculate the square of the original...

Homework Statement Find [(3 - 51/2)/2]1/2 Homework EquationsThe Attempt at a Solution My calculator says (-1 + √5)/2 I have no idea how. Rationalising doesn't really do much good. Just tell me where to start.

Homework Statement 2*3*4*5/4+3*4*4*6 Homework Equations 2*3*4*5/4+3*4*4*6 The Attempt at a Solution 2*3*5/1+3*4*6 Knowledge gap 1 - I do not understand why if top and bottom are divided through by 4 there should be a 4 left in the denominator and why the rest of the numerators and...

Homework Statement To simplify: ##\mid \vec b -\frac{\vec a*\vec b}{\vec a*\vec c} * \vec c \mid## ##\mid \vec b -\frac{(\vec a*\vec c)*(\vec b*\vec b)-(\vec a*\vec b)*(\vec b*\vec c)}{(\vec a*\vec b)*(\vec c*\vec c)-(\vec a*\vec c)*(\vec b*\vec c)} * \vec c \mid## Vectors may be any...

Homework Statement Simplify (6x+12y)/(10a +5) times (100a2 - 25)/(9x2 - 81y2) Homework Equations (6x+12y)/(10a +5) times (100a2 - 25)/(9x2 - 81y2) The Attempt at a Solution (6x+12y)/(10a +5) times (100a2 - 25)/(9x2 - 81y2) = 3(2x+4y)/(10a+5) times (4a - 1)/(3x-27y) =...

Homework Statement Simplify: (a2 + 2ab + b2)/(a2 - b2) times (a2 - 2ab + b2)/(a2 - b2) Homework Equations (a2 + 2ab + b2)/(a2 - b2) times (a2 - 2ab + b2)/(a2 - b2) The Attempt at a Solution Did I simplify this correctly?? (a+b)(a+b)/((a-b)(a+b)) times (a-b)(a-b)/((a-b)(a+b)) = ((a+b)/(a+b))...

Folks, Just struggling to see how this is simplified. \frac{f''(x)}{((1+f'(x)^2)^{1/2}}-\frac{f'(x)^2 f''(x)}{((1+f'(x)^2)^{3/2}}=\frac{f''(x)}{((1+f'(x)^2)^{3/2}} if we let a=(1+f'(x)^2)^{1/2} then I get as far asf''(x)[a^{-1/2}-f'(x)^2a^{-3/2}]=f''(x)[a^{-1/2}-f'(x)^2 a^{-1/2} a^{-1}]...

Homework Statement Sorry for the pictures, I'd normally write out the problem but it is mostly diagrams. Question and work attached. I am looking for help with part (a) right now, the transfer function I obtain is shown at the end of my work. Homework Equations Knowledge of Laplace transforms...

Homework Statement The problem is to sketch lines of constant u and v in the image plane for the function Log[(z+1)/(z-1)]. Homework Equations z=x+iy The Attempt at a Solution In order to do this I have to get the expression into u+iv form, so that I can read off and manipulate the u and v...

So, I have an equation: ~A * B * C * ~D + ~A * B * C * D + A * ~B * ~C * D + A * ~B * C * D + A * B * ~C * D + A * B * C * ~D where * represents "AND" and + represents "OR", ~ being NOT. Part of the reason I'm having trouble is due to the length of the equation. So far, I've managed to use...

Given that we have the expression ##\displaystyle-\frac{1}{(x-2)(x-2)(x-3)}~\cdot~\sqrt{\frac{(x-2)^{2}}{(x-3)(x-1)}} ##, how do we simplify it, step by step? Specifically, I am concerned about the ##\sqrt{(x-2)^{2}}## term. Are we allowed to cancel this with the ##(x-2)## in the denominator?

$$\frac{\cot^3\left({y}\right)-\tan^3\left({y}\right)} {\sec^2\left({y}\right)+\cot^2\left({y}\right)} =2\cot\left({2y}\right)$$ I tried the LHS but could get it to reduce.

I do not understand this even the one in Wikipedia. Can anyone explain it to me as simple as possible as well as give me some simple examples? Thanks a lot!

Hello, I am very new to tensors and GR and would like to ask for guidance to understand how tensor simplification works. If we have this term $$\frac{1}{2}N_{IJ}F_{\mu\nu}^I\tilde{F}^{J\mu\nu} $$ and I want to derive w.r.t ##F^{\rho\sigma I}## where - ##N_{IJ}## is a symmetric complex matrix -...

Homework Statement [/B] Hi, I am currently working through a textbook, and the following simplification is given for an example question: I can't seem to work out how they have moved from cos(pi+n*pi) to cos(pi)cos(n*pi) so easily? Is there a simple trick I have missed? I understand the...

This is take 2.0 of the earlier thread, which got a lot of help from George J., Jorrie, Wabbit, Ken G, and others. I'm exploring this simplification of the flat matter-dominated ΛCDM model (basically anything after year 1 million) to see if there is a presentation that would be suitable for PF...

Simplify the expression $\dfrac{\sqrt{1+\sqrt{1-a^2}}((1+a)\sqrt{1+a}-(1-a)\sqrt{1-a})}{a(2+\sqrt{1-a^2})}$.

Calculate ( minus ( 2 over 3 ) + ( 2 over 3 ) i ) to the power minus 4, simplifing your answer and giving it in the form a + i b, with a and b given exactly.I found the modulus by: sqrt((-2/3)^2 + (2/3)^2) = (2*sqrt(2))/3 the argument is: pi - 1 (from a sketch in the complex plane) hence...

So let me start off by saying I am horrible at math and always have been. Despite considering myself highly intelligent, I suck at math. It's what led me into computer programming instead of physics like I wanted. Simply, I want to ask, say I have a fraction or a ratio that can't be simplified...

Simplify the expression below: $\dfrac{w^2(z-x)(z-y)}{(w-x)(w-y)}+\dfrac{x^2(z-y)(z-w)}{(x-y)(x-w)}+\dfrac{y^2(z-w)(z-x)}{(y-w)(y-x)}$

Okay guys, this is driving me absolutely nuts. I'm working on finding derivatives using the product and quotient rules and the book will sometimes simplify the problem before finding the derivative but sometimes wont and I don't understand why. For example: The function y = (v3-2v√v)/v The book...